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Unformatted text preview: Worksheet 6 Math 126 (best if discussed in small groups) This worksheet gives an example of estimating a double integral by Riemann sums, and shows the benefit of using linearity. 1. Figure 1 is a (somewhat crude) topographical map of Mt. St. Helens in 1979, prior to the eruptions. The curves are level lines. The numbers near each level line give the altitude or elevation of the mountain above the level line. If h ( x, y ) denotes the altitude above the point ( x, y ), then why does integraltext integraltext R h ( x, y ) dxdy represent the volume of the mountain above the region R ? (Hint: how is this integral defined?) 2. Figure 2 is a topographical map in 1998, after the eruptions. Where on the map is the mountain unchanged and where is it changed? Where is the new mountain very steep? The base of the crater has elevation slightly more than 2000m. 3. If k ( x, y ) denotes the altitude of the mountain above the point ( x, y ) then the loss of volume is given by: L = integraldisplay integraldisplay...
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